Light scattered from an object contains both amplitude and phase information. This amplitude and phase information can be captured on, for example, a photosensitive plate by well known interference techniques to form a holographic recording, or “hologram”, comprising interference fringes. The “hologram” may be reconstructed by illuminating it with suitable light to form a holographic reconstruction, or image, representative of the original object.
It has been found that a holographic reconstruction of acceptable quality can be formed from a “hologram” containing only phase information related to the original object. Such holographic recordings may be referred to as phase-only holograms or kinoforms.
The term “hologram” therefore relates to the recording which contains information about the object and can be used to form a reconstruction representative of the object. The hologram may contain information about the object in the frequency, or Fourier, domain.
Computer-generated holography is a technique to numerically simulate the interference process, it may use Fourier techniques for example, to produce a computer-generated phase-only hologram. The computer-generated phase-only hologram may be used to produce a holographic reconstruction representative of an object.
It has been proposed to use holographic techniques in a two-dimensional image projection system. The system may accept a temporal sequence of 2D image frames as an input. The input may be converted into a real-time sequence of corresponding holograms (for example, phase-only holograms) wherein each hologram corresponds to one image frame. The holograms may be reconstructed in real-time on a screen to produce a 2D projection representative of the input. Accordingly, there may be provided a real-time 2D video projector to project a sequence of image frames using a sequence of computer-generated holograms.
An advantage of projecting video images via phase-only holograms is the ability to control many image attributes via the computation method—e.g. the aspect ratio, resolution, contrast and dynamic range of the projected image. A further advantage of phase-only holograms is that no optical energy is lost by way of amplitude modulation.
A computer-generated phase-only hologram may be “pixellated”. That is, the phase only hologram may be represented on an array of discrete phase elements. Each discrete element may be referred to as a “pixel”. Each pixel may act as a light modulating element such as a phase modulating element. A computer-generated phase-only hologram may therefore be represented on an array of phase modulating elements such as a liquid crystal on silicon (LCOS) spatial light modulator (SLM). The LCOS may be reflective meaning that modulated light is output from the LCOS in reflection.
Each phase modulating element, or pixel, may vary in state to provide a controllable phase delay to light incident on that phase modulating element. An array of phase modulating elements, such as a LCOS SLM, may therefore represent (or “display”) a computationally determined phase-delay distribution. If the light incident on the array of phase modulating elements is coherent, the light will be modulated with the holographic information, or hologram. The holographic information may be in the frequency, or Fourier, domain.
Alternatively, the phase-delay distribution may be recorded on a kinoform. The word “kinoform” may be used generically to refer to a phase-only holographic recording, or hologram.
The phase-delay distribution may be applied to an incident light wave (by illuminating the LCOS SLM, for example) and reconstructed. The position of the reconstruction in space may be controlled by using a optical Fourier transform lens, to form the holographic reconstruction, or “image”, in the spatial domain.
A computer-generated hologram may be calculated in a number of ways, including using algorithms such as Gerchberg-Saxton. The Gerchberg-Saxton algorithm may be used to derive phase information in the Fourier domain from amplitude information in the spatial domain (such as a 2D image). That is, phase information related to the object may be “retrieved” from intensity, or amplitude, only information in the spatial domain. Accordingly, a phase-only holographic representation of an object in the Fourier domain may be calculated.
The holographic reconstruction may be formed by illuminating the Fourier domain hologram and performing an optical Fourier transform using a Fourier transform lens, for example, to form an image (holographic reconstruction) at a reply field such as on a screen.
FIG. 1 shows an example of using a reflective SLM, such as a LCOS, to produce a holographic reconstruction at a replay field location, in accordance with the present disclosure.
A light source (110), for example a laser or laser diode, is disposed to illuminate the SLM (140) via a collimating lens (111). The collimating lens causes a generally planar wavefront of light to become incident on the SLM. The direction of the wavefront is slightly off-normal (i.e. two or three degrees away from being truly orthogonal to the plane of the transparent layer). The arrangement is such that light from the light source is reflected off a mirrored rear surface of the SLM and interacts with a phase-modulating layer to form an exiting wavefront (112). The exiting wavefront (112) is applied to optics including a Fourier transform lens (120), having its focus at a screen (125).
The Fourier transform lens receives (phase modulated) light from the SLM and performs a frequency-space transformation to produce a holographic reconstruction at the screen (125) in the spatial domain.
In this process, the light from the light source is generally evenly distributed across the SLM (140), and across the phase modulating layer (array of phase modulating elements). Light exiting the phase-modulating layer may be distributed across the screen. There is no correspondence between a specific image region of the screen and any one phase-modulating element.
The Gerchberg Saxton algorithm considers the phase retrieval problem when intensity cross-sections of a light beam, IA(x,y) and IB(x,y), in the planes A and B respectively, are known and IA(x,y) and IB(x,y) are related by a single Fourier transform. With the given intensity cross-sections, an approximation to the phase distribution in the planes A and B, ΦA(x,y) and ΦB(x,y) respectively, is found. The Gerchberg-Saxton algorithm finds good solutions to this problem by following an iterative process.
The Gerchberg-Saxton algorithm iteratively applies spatial and spectral constraints while repeatedly transferring a data set (amplitude and phase), representative of IA(x,y) and IB(x,y), between the spatial domain and the Fourier (spectral) domain. The spatial and spectral constraints are IA(x,y) and IB(x,y) respectively. The constraints in either the spatial or spectral domain are imposed upon the amplitude of the data set. The corresponding phase information is retrieved through a series of iterations.
It is desirable to provide a method of phase retrieval which can be implemented in a way that provides convergence more rapidly than the prior art.